Prediction of Responses for Simarouba Biodiesel based CRDI Engine using General Regression Neural Network

: The evaluation of performance and emission of Common Rail Direct Injection (CRDI) engine fuelled by various biodiesel at different operating conditions is time consuming and expensive. This can be overcome by using prediction techniques like GRNN. The GRNN model is developed using ‘newgrnn’ function in Matlab R2019b software to predict the performance and emission responses of CRDI engine for simarouba biodiesel. A total of 27 experimental dataset of each biodiesel is used for development of model. Out of 27 experimental dataset, 21 datasets are selected randomly for training the model. The remaining 6 datasets are utilized for testing the GRNN model. In this study, 20 different values of spread parameters within the range 0.05 to 1 with step increment of 0.05 are chosen. As a result, 20 simulations are performed and the best predicted results are chosen based on least mean error. The optimum spread parameter for simarouba, pongamia and composite biodiesel GRNN model was found to be 0.1, 0.1 and 0.05 respectively. The Root Mean Square Error (RMSE) values of different responses are found to be acceptable. The results indicated that GRNN model for the prediction of engine responses yields good correlation with experimental values and are acceptable for new predictions.


Introduction
India is one of the fastest developing countries in the world with a stable economic growth whose objective focusses on equity, growth and well-being of humans. Energy serves as indispensable input for socio economic development of developing countries [1]. India imports fossil fuels to satisfy its energy requirement and the demand will continue to rise in the near future [2]. Fossil fuels are limited, non-renewable and polluting and therefore, they have to be used cautiously. The continuous use of fossil fuels will make it eventually depleting and there is a need to search for alternate fuels.
In India, majority of population is relied upon agriculture for their livelihood and problems of rural areas could be solved to a larger extent by promoting the biofuels in rural regions. Since India is an agrarian nation, extensive opportunity is available for biodiesel production from different tree borne oil seeds. India is still highly dependent on foreign countries for its domestic requirement of edible oil, hence it is not considered as best promising feedstock for biodiesel production. In this context, fuels derived from biodiesel feedstocks especially nonedible oils could become potential game changer. A wide variety of potential nonedible oil seeds are available across India and some are grown predominantly based on geographical locations [3]. However, many potential non-edible oils are yet to be explored as feedstocks for biodiesel. Therefore, this work is focussed on the use of simarouba non-edible oil as an alternate fuel to diesel in CRDI engine. Simarouba oil is processed through two stage transesterification process using methanol and sodium hydroxide / concentrated sulphuric acid as a catalyst to produce biodiesel. The experimentation is conducted on CRDI engine using B5, B10 and B20 blends of simarouba, biodiesel. The evaluation of performance and emission of CRDI engine fuelled by various biodiesel at different operating conditions is time consuming and expensive. During research, it is observed that lot of time and resources are wasted to carry out all the experiments for each biodiesel blend. This can be overcome by using prediction techniques like GRNN. From the literature review it is found that only few authors have used GRNN for engine applications. Therefore an effort is made to implement General Regression Neural Network (GRNN) for the prediction of engine performance and emission responses.

General Regression Neural Network (GRNN)
GRNN is recommended by D.F Specht, which is a feed forward supervised type network used for regression and function approximation. This network uses radial basis activation function [4]. It is a memory based highly parallel structure network which learns from the training data in a single pass [5,6,7]. When training is done on GRNN network, it memorizes unique patterns in the training data. Once training is completed, GRNN can generalize for the new input data with high accuracy. Since GRNN is one pass training algorithm, there is no concept of training the weights as in the case of other networks. Thus, in GRNN, there are no learning rates and initial weights [10,11].
GRNN is basically used for function approximation and is based on the probability density function of predictor variable X and response variable Y. The GRNN will predict the output Y for any values of input X in a short duration. In GRNN, the prediction of output Y is estimated using Eq. 1.
Where (Xi, Yi) represents the sample of (X, Y), Y(x) is the estimated value, Di is the Euclidean distance among input X and training sample input Xi, σ is the smoothing parameter or spread parameter or Gaussian Width (GW), which denotes the width of radial basis function and n represents the quantity of training samples,. Euclidean distance is determined using Eq. 2. The estimate Y(x) denotes the weighted average of all the sample values Yi, where the exponential of squared Euclidean distance between X and Xi gives the weight for each sample.
Euclidean distance (D 2 i) signifies the contribution of training sample to the output of GRNN. Smaller value of D 2 i contributes more to the output with larger exp (-D 2 i/ 2σ 2 ) value and larger D 2 i value gives less contribution to the output with smaller exp (-D 2 i/ 2σ 2 ) value. If D2i becomes zero, then test data completely matches with training sample data and predicted value by GRNN will be output of training sample. The term exp (-D 2 i/ 2σ 2 ) is the output of hidden layer neuron. Therefore, GRNN allocates the target Yi to the weights obtained from the training sample. But weights are trained several times in other neural networks like BPNN until error becomes less. The term exp (-D 2 i/ 2σ 2 ) in Eq. 1 contributes more to the predicted output of GRNN [8]. In GRNN, spread parameter or smoothing parameter or GW is the critical parameter which needs to be determined by the user and its value affect the performance of network [9]. The value of spread parameter affects the accuracy of prediction. There are no proper models to find optimum σ, trial and error approach is employed in this study to determine σ.

Methodology
Experiments to be conducted are designed using Taguchi Design of Experiments (DOE) with L9 orthogonal array considering three engine control factors viz., injection pressure (IP), injection timing (IT) and fuel preheating temperature (FPT). Each factor is varied at three levels i.e., 400 bar, 500 bar and 600 bar are the levels for injection pressure, 21˚ bTDC, 23˚ bTDC and 25˚ bTDC are the levels for IT and 30˚ C, 40˚ C and 50˚ C are the levels for FPT. From the experimentation, performance responses such as brake thermal efficiency and brake specific fuel consumption and emission responses such as CO, CO2, UHC and NOx will be evaluated.

Fig. 1 Input and Output Parameters of GRNN model
The schematic overview of GRNN model used for the prediction of responses of CRDI engine is shown in Fig. 1. Fig. 2 shows the GRNN architecture used in the present study for the prediction of CRDI engine performance and emission responses. Out of 27 experimental dataset of biodiesel, 21 datasets are used for training the model which is selected randomly and remaining 6 datasets are used for testing the model. The blend percentage of biodiesel along with the engine control factors such as IP, IT and FPT are selected as input parameters for the model. These parameters are considered as they affect the performance of engine significantly.

Fig. 2 Architecture of GRNN for Prediction of CRDI Engine Responses
Step 1: A total of 27 experimental data of CRDI engine are used and 80% of data is dedicated for training and 20% of data is used for testing the GRNN model. Step 2: The experimental data sets are normalized by decimal scaling technique before training and testing the GRNN model. Step 3: The code is written on Matlab R2019b platform to build GRNN. Denominator summation neuron finds average of weights for all experimental data sets (i=27). Additional neuron is used to find the output of probability density function. The predicted outputs for all the responses are determined in output layer using Eq. 1.
Step 5: The network is simulated again for different values of spread parameter and 20 simulations are performed and predicted outputs of all the simulations are stored in the variable (y3).
Step 6: The mean error is computed for all the 20 simulations by comparing predicted output with actual values. The best prediction model is selected based on minimum mean error and optimum σ is obtained. Step 7: The performance of GRNN model is evaluated by using RMSE as performance metric. Then, the GRNN model can be deployed for the prediction of new data sets.

Experimental Setup
The experiments are carried out on CRDI engine with an open ECU set up using B5, B10 and B20 blends of simarouba biodiesel. Fig. 3 shows the CRDI engine setup. The technical details of the CRDI engine are presented in the Table 1. Fig.4 shows the AVL five gas analyzer which is used for the measurement of emission responses.

Results and Discussion
The GRNN model is built using 'newgrnn' function in the Matlab software. The standard syntax for newgrnn function is as follows: Syntax for GRNN model design: net = newgrnn (tr, tar, spread parameter) GRNN takes three inputs namely training data, target data and spread parameter value. The training dataset is imported into Matlab platform. The variable 'tr' stores the input values and variable 'tar' stores the target values of training dataset. The supervised training i.e., labelled training datasets is used in this present study. After training, model is deployed to predict the output of new datasets. The codes are executed, which runs the function 'newgrnn' by taking all the inputs and results in optimized network.
During training of GRNN, the value of σ is varied between 0.05 -1 in steps of 0.05 for finding an optimum σ. Thus a total of 20 simulations are performed. The iterative process of learning of weights and spread parameters are achieved in the network. Each network predicts the output based on spread parameter and training data. The best network model is selected based on the minimum mean error, which is calculated between network output and actual experimental values of testing datasets.
In the present study, General Regression Neural Networks (GRNN) model is developed for the prediction of performance and emission responses of CRDI engine fuelled with B5, B10 and B20 blends of simarouba biodiesel. GRNN model is developed to predict the performance and emission responses of CRDI engine. Table 2 and Table 3  software, which automates the learning process and testing of model. The prediction accuracy of GRNN model is found to be nearly 100% during training for all the biodiesel.  The GRNN model obtained for different spread parameters for Simarouba biodiesel are analyzed. The effect of spread parameter on GRNN prediction is as shown in Fig. 5. It is observed from the graph that the performance of network is affected by variation in the value of σ. Larger value of σ leads to higher mean error for the network due to overlapping of neurons and firing for the same input. The model with spread parameter of 0.1 shows the least mean error for the engine responses. Hence this is considered to be the optimum spread value. Table 4 shows the predicted values of engine responses by GRNN model for Simarouba Biodiesel. Fig. 6 to Fig. 11 shows the scatter diagram for the comparison of predicted values with actual experimental values of different responses. It is observed that GRNN model prediction for BTE, BSFC, CO and CO2 are strongly correlating with actual values. The RMSE of these parameters are found to be 0.587 %, 0.0082 kg/kWh, 0.0969 % and 0.0695 % respectively. Also it is observed that GRNN prediction for UHC and NOX results in RMSE of 5.180 ppm and 29.89 ppm respectively. The prediction ability of GRNN may be improved further for parameters especially UHC and NOX by considering more training datasets. Thus, it is inferred that the prediction results of GRNN model are very much correlated and found to be promising for new datasets.

Conclusion
The evaluation of performance and emission of CRDI engine at different operating conditions is time consuming and expensive. Therefore, GRNN is implemented to predict the performance and emission responses of CRDI engine running with biodiesel. It is found that GRNN model has resulted in 100% prediction accuracy for training datasets. From the analysis of GRNN results, it can be concluded that the prediction of responses has good correlation with experimental values for all the testing cases. Therefore, GRNN can be considered as powerful neural network technique for the prediction of engine responses. The performance of GRNN model can be further improved by considering more data samples of CRDI engine.